A group of 5 students is to be chosen from a class of
20 students to work on a term project. How many different groups of
students can be chosen from the class?
20C5 = (20*19*18*17)/(1*2*3*4*5)
4
The answer is straight out 4!
shown work
20-5=15 5 = 1group
20 divided by 5 equals 4
To calculate the number of different groups of students that can be chosen from a class of 20 students to work on a term project, we can use the concept of combinations.
The formula for calculating the number of combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items to choose from and r is the number of items to be chosen.
In this case, we have 20 students to choose from (n = 20) and we need to choose a group of 5 students (r = 5).
Plugging these values into the formula:
C(20, 5) = 20! / (5! * (20 - 5)!)
Simplifying:
C(20, 5) = 20! / (5! * 15!)
Since 15! can be canceled out from both the numerator and denominator:
C(20, 5) = (20 * 19 * 18 * 17 * 16) / (5 * 4 * 3 * 2 * 1)
Calculating this expression, we get:
C(20, 5) = 15,504
Therefore, there are 15,504 different groups of students that can be chosen from the class of 20 students to work on a term project.
To find out how many different groups of students can be chosen from the class, we need to calculate the number of combinations.
In this case, we have 20 students to choose from, and we want to form a group of 5 students. The order in which the students are chosen does not matter, so we use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n - r)!)
Where:
- n is the total number of items to choose from
- r is the number of items to be chosen
In this case, we have 20 students to choose from (n = 20) and we want to choose a group of 5 students (r = 5).
Plugging the values into the formula, we get:
C(20, 5) = 20! / (5!(20 - 5)!)
Now, let's calculate the result step by step:
20! = 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
5! = 5 × 4 × 3 × 2 × 1
(20 - 5)! = 15!
Now, we can simplify the expression:
C(20, 5) = (20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((5 × 4 × 3 × 2 × 1) × (15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1))
By simplifying the expression, most factors cancel out:
C(20, 5) = (20 × 19 × 18 × 17 × 16) / (5 × 4 × 3 × 2 × 1)
Calculating the remaining factors:
C(20, 5) = (20 × 19 × 18 × 17 × 16) / (5 × 4 × 3 × 2 × 1)
C(20, 5) = 15,504
Therefore, there are 15,504 different groups of students that can be chosen from the class.